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DOCUMENT RESUME ED 194 317 SE 033 066 Mathematics DOCUMENT RESUME ED 194 317 SE 033 066 TITLE Mathematics Evaluation Procedures K-2. For Use by Teachers With Children in Years K-4. INSTITUTION Australian Council for Educational Research, Hawthorn. FEPORT NO ISBN-0-85563-210-0 PUB DATE Sep BO NOTE 279p.: Not available in hard copy due to copyright restrictions. Contains occasional marginal legibility. Prepared in collaboration with the North Sydney Region Infants Mistresses Council. AVAILABLE FROMLawrence Verry, Inc., River Road, CT 06355 (no price quoted). EDRS PRICE MF01 Plus Postage. PC Not Available from EDRS. rESCEIPTORS Academic Achievement: *Cognitive Measurement; Diagnostic Tests: Elementary Education: *Elementary School Mathematics: Evaluation; *Evaluation Methods: *Learning: *Mathematics Instruction; Resource Materials: Student Characteristics; *Testing ABSTRACT This book was written in response toa need expressed by Infant's Mistresses in the North Sydney Region of the NewSouth Wales Department of Education. They felt therewas a need to evaluate children's progress in mathematics in order to diagnose thecauses of individual failures, and they discovered there was no readily available information on either what or how to test. A committeewas appointed to investigate and rectify the situation. Goals selected were a massive list of learning objectives, and approximately five test items. per objective were constructed. This document consists of instructions and information cn testing, selected notes and comments, the tests, an appendix on trialling, and sample studentresponse sheet forms, the product of several years of work. The testsare devised for administering to individual elementary schoolpupils in grades K -4 with the object of observing theresponses of those pupils. The tests are set out in continuous form withoutage or grade labels, and are organized within three broad categories ofnumber, shape, and measurement. (MP) *********************************************************************** * Reproductions supplied by EDRS are the best that can be made * * from the original document. * *********************************************************************** Published by The Australian Council for Educational Research Limited Radford House, Frederick Street, Hawthorn, Victoria, 3122 Printed and bound by Brown Prior Anderson Pty Ltd Burwood, Victoria, 3125 National Library of Australia Cataloguing-in-Publication data. Mathematics evaluation procedures, K-2. Previously published, North Sydney, N.S.W.: North Sydney Region Infants' Mistresses' Council, 1979. ISBN 0 85563 210 0 1. Number conceptAbility testing. 2. Education, Primary. I. North Sydney Region Infants' Mistresses' Council. II. Australian Council for Educational Research. 372.7'2044 Copyright © North Sydney Region Infants' Mistresses' Council No part of this publication may be reproduced in any form without permission fro the publisher. II ACKNOWLEDGEMENTS The North Sydney Region Infants' Mistresses' Council acknowledges the assistance of the following people and thanks them for their efforts. Mr. Tom Reid, B.A., Director of Education, North Sydney Region, who has given his support and encouragement throughout this project. Mr. Ted King, M.A., Inspector of Schools, Chairman of North Sydney Region Development Committee, whose help in making In-service facilities available has been invaluable. Mr. Sid Bourke, B.A., B.Sc., Litt.B., Chief Research Officer, Australian Council for Educational Research, whose guidance and advice have been greatly appreciated. Dr. Bob Phillips, B.A., Ph.D.,-Head of the Department of Teaching and Curriculum Studies, Alexander Mackie College of Advanced Education, who began the whole project with his talk to our conference in 1974, and maintained a continuing interest in the project. Mrs. Elaine Callan, Mrs. Marie Muir and Miss Kath Yabsley, Committee members, who have been primarily concerned in selecting the evaluation goals and compiling the test items, also Mrs. Jan Hodge and Miss Jan Watt who were part of the committee in the early stages when the goals were being listed. The people who were involved in putting together the Trialling Document, all those who typed, duplicated and collated, and especially the staff at Alexander Mackie C.A.E. who stapled and bound all the copies for use. All the mathematicians, educationists and college lecturers who read, considered and checked the draft document and gave the committee the benefit of their specialised knowledge, particularly Mr. Alex Aitkin, M.Sc., formerly of Sydney Teachers College, whose thorough perusal and informative comments were much appreciated, Mrs. Nita Hughes, M.A., Dip.Ed., Senior Lecturer, Mathematics, Primary Programme Director, Sydney Teachers College, who made many pertinent comments on the text, and Miss Joan Sutton, B.A., M.Ed., Inspector of Schools, who gave help in assessing conservation activities. Those who sent to the Committee their written comments on the draft document: Mr. Eric R. Ashcroft, MA., Dip.T., Senior Lecturer, Education Department, Massey University, Palmerston North, N.Z., Mr. W. Barry, M.A., Head of Mathematics, Alexander Mackie College of Advanced Education, Ms. B. Dunbar, B.Ed., Central Metropolitan Region Primary Mathematics Consultant, Professor Wilbur H. Dutton, A.B., M.A., Ed.D., (Emeritus 1948-197-5) Department of Education, University of California, Los Angeles, U.S.A., Mr. W.L. Howard, B.A., M.Ed., Newcastle College of Advanced Education, Mr. Peter Jeffery, B.A., B.Ed., Senior Advisory Officer, Education Advisory Services A.C.E.R., and Mrs. Irene Sawczak. who assisted Mr. Jeffery. iii The mathematics students of Alexander Mackie College of Advanced Education and of Sydney Teachers' College, who carried out assignments on the test procedures and whose insightful comments were most helpful, also their lecturers, Bob Phillips and Nita Hughes, respectively, who guided them in their work. Mrs. Joan Graham, w helped the Committee during the early stages in the formulation of the goals. Dr. Robert Perry, B.Sc., Dip.Ed., Ph.D., Mitchell College of Advanced Education, who co-ordinated trialling in the one-teacher schools of the Bathurst area. Mr. Kevin Earl, Publications Officer, Alexander Mackie College of Advanced Education, who gave helpful advice on publication procedures. The Mistresses, Principals and class tecchers of the schools where trialling was carried out, who worked on the tests, recorded their comments, met with the committee, offered their suggestions and gave their opinions, and so shaped the final form of the book. Lastly all the children who were the "guinea-pigs" for the trial testing, whose responses were diagnosed, and whose progress was analysed, so that many other children may in the future be helped to mathematical competence through use of these tests. iv CONTENTS Page Acknowledgements iii Index of Objectives Number vii Shape Measurement Introduction 1 Instructions and Information Testing 3 Approach 3 Purposes 3 Format 4 Materials 5 Administration 6 Assessment 7 Recording Responses 8 Suggested Form for Response Sheet 9 Filling in a Response Sheet 11 Interpretation of Marking 12 Follow-up 12 Notes and Comments Advantages of Testing 13 The Time Taken in Testing 14 Common Causes of Failure 15 Testing Beyond Grade Level 16 Suggested Grade Levels for Diagnostic Testing 16 Memorization, Problem Work, Graphs 19 Use of "Crutch" Figures 19 "Number" Bias 20 Conservation 20 Geheral Knowledge 21 Prompting 21 Wrong Responses 22 Notes and Comments (continued) Page How Many Times? Size of the Book 23 Why "Sets" and "Subsets"? 23 The Tests Number 26 Memorization 113 Problems 128 Graphs 148 Shape 156 Measurement Length 169 Mass 185 Volume (Capacity) 198 Area 212 Time 221 Money 231 Temperature 239 Appendix Outline of Trialling Feedback 242 Documents 257 Response Sheet Forms 263 7 vi INDEX NUMBER No. OBJECTIVES. Test items begin The Child ... on page NUMBER. 1. Identifies attributes 26 2. Classifies an object by means of its attributes 26 3. Sorts objects 28 4. Makes given sets 5. Pairs the elements of one set with the elements of another set, and finds whether two sets match or do not match by using the technique of pairing 30 6. Understands that two equivalent sets remain equivalent however the members of each set are re-arranged 32 7. Counts the members of a set 33 8. Finds the cardinal number of a sei 33 9. Makes a set containing a given number of elements 34 10. Matches numeral with cardinal number 35 11. Writes numeral for cardinal number of a set 37 12. Uses ordinal numbers 37 13. Orders sets (counting order) 40 14. Understands the relationship of one set to the next in the counting order 41 15.Understands that a set has the same cardinal number when the members are re-arranged 42 16. Understands and uses the terms "more" and "less" through comparison of sets 43 17. Understands that all sets which arc equivalent have the same cardinal number 47 18. Understands the meaning of, and writes, the equals sign 50 19.Separates a set into subsets and understands the part-whole relationship . 53 20.Knows that zero is the cardinal number and nought is the numeral for the set that has no members 58 21.Combines two sets to form a new set and understands that this is an action of addition 60 vii INDEX NUMBER No. OBJECTIVES. Test items begin The Child.,. on page NUMBER (continued). 11 Understands that whatever the order in which sets are combined, the total number of members is the same 63 23. Separates a set into two subsets. removes one subset and understands that this is an action of sohtraction 64 24. Compares two sets by pairing to find the difference between them, and understands that this is also an action of subtraction 67 15. Understands that there is an inverse relationship between the operations of addition and subtraction, and of subtraction and addition 69 26. Understandsthatfrom one additionfact,other additionfacts and subtraction facts can be derived 71 '7. Combines several sets each with the same cardinal number to form a new set and understandsthatthisactionofrepeatedadditionis multiplication 74 '8. Partitions a set into two equivalent subsets and understands that this is the action for finding halves 76 29. Understands and uses the terms "odd and "even'' 79 30.
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